A Markov-modulated tree-based gradient boosting model for auto-insurance risk premium pricing

2020 ◽  
Vol 8 (1-2) ◽  
pp. 1-13
Author(s):  
Dennis Arku ◽  
Kwabena Doku-Amponsah ◽  
Nathaniel K. Howard
Keyword(s):  
Risk Premium ◽  
Gradient Boosting ◽  
Insurance Risk ◽  
Auto Insurance ◽  
Markov Modulated

scholarly journals Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model

2005 ◽  
Vol 35 (02) ◽  
pp. 351-361 ◽  
Author(s):  
Andrew C.Y. Ng ◽  
Hailiang Yang
Keyword(s):  
Regime Switching ◽  
Joint Distribution ◽  
Risk Model ◽  
Insurance Risk ◽  
Additive Process ◽  
Deficit At Ruin ◽  
Markov Additive Process ◽  
The Deficit At Ruin ◽  
Markov Modulated ◽  
Markovian Regime Switching

In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.

Fluctuation identities for Omega-killed spectrally negative Markov additive processes and dividend problem

2020 ◽  
Vol 52 (2) ◽  
pp. 404-432
Author(s):  
Irmina Czarna ◽  
Adam Kaszubowski ◽  
Shu Li ◽  
Zbigniew Palmowski
Keyword(s):  
Insurance Risk ◽  
Additive Process ◽  
Markov Additive Process ◽  
Surplus Process ◽  
Current State ◽  
Markov Modulated ◽  
Exit Problems ◽  
State Of The Environment ◽  
Risk Processes ◽  
Omega Model

AbstractIn this paper, we solve exit problems for a one-sided Markov additive process (MAP) which is exponentially killed with a bivariate killing intensity $\omega(\cdot,\cdot)$ dependent on the present level of the process and the current state of the environment. Moreover, we analyze the respective resolvents. All identities are expressed in terms of new generalizations of classical scale matrices for MAPs. We also remark on a number of applications of the obtained identities to (controlled) insurance risk processes. In particular, we show that our results can be applied to the Omega model, where bankruptcy takes place at rate $\omega(\cdot,\cdot)$ when the surplus process becomes negative. Finally, we consider Markov-modulated Brownian motion (MMBM) as a special case and present analytical and numerical results for a particular choice of piecewise intensity function $\omega(\cdot,\cdot)$ .

scholarly journals Insurance offer and the reason for the underdeveloped market in Serbia

2020 ◽  
Vol 8 (4) ◽  
pp. 51-59
Author(s):  
Milorad Pušara
Keyword(s):  
Risk Premium ◽  
Technology Development ◽  
Business Management ◽  
Developed Countries ◽  
World Market ◽  
Insurance Market ◽  
Insurance Risk ◽  
The World ◽  
The Developed Countries ◽  
Good Standard

This paper presents the current condition of the insurance market by creating an unpretentious review and pointing to the current deficiency of the insurance system in Serbia. It outlines some ideas that might solve certain issues and improve the current situation. Referred innovations that were introduced last year in the world market are very useful and can also serve as a good standard for joining the global insurance. Last but not least, the paper addresses the segment of insurance frauds as alarming incidences in need of attention. If we consider the "Basic Elements of Insurance", risk, premium, and indemnity, and if we follow the development of the insurance throughout the world, we recognize that technology development and reduced business costs imply greater risks, a growing range of new products, decreased premium, and stimulating increase of the Indemnity. This leads us to the conclusion that we must enter the race with the developed countries and accept the way of their business management by following the latest innovations in the insurance market in order to be competitive and competent.

scholarly journals On Exceedance Times for Some Processes with Dependent Increments

2014 ◽  
Vol 51 (01) ◽  
pp. 136-151 ◽  
Author(s):  
Søren Asmussen ◽  
Sergey Foss
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Risk Process ◽  
Fluid Models ◽  
Insurance Risk ◽  
Heavy Tailed Distribution ◽  
Negative Drift ◽  
Time Position ◽  
Heavy Tailed ◽  
Markov Modulated

Let {Z n } n≥0 be a random walk with a negative drift and independent and identically distributed increments with heavy-tailed distribution, and let M = sup n≥0 Z n be its supremum. Asmussen and Klüppelberg (1996) considered the behavior of the random walk given that M > x for large x, and obtained a limit theorem, as x → ∞, for the distribution of the quadruple that includes the time τ = τ(x) to exceed level x, position Z τ at this time, position Z τ-1 at the prior time, and the trajectory up to it (similar results were obtained for the Cramér-Lundberg insurance risk process). We obtain here several extensions of this result to various regenerative-type models and, in particular, to the case of a random walk with dependent increments. Particular attention is given to describing the limiting conditional behavior of τ. The class of models includes Markov-modulated models as particular cases. We also study fluid models, the Björk-Grandell risk process, give examples where the order of τ is genuinely different from the random walk case, and discuss which growth rates are possible. Our proofs are purely probabilistic and are based on results and ideas from Asmussen, Schmidli and Schmidt (1999), Foss and Zachary (2002), and Foss, Konstantopoulos and Zachary (2007).

scholarly journals The Resolvent and Expected Local Times for Markov-Modulated Brownian Motion with Phase-Dependent Termination Rates

2013 ◽  
Vol 50 (2) ◽  
pp. 430-438 ◽  
Author(s):  
Lothar Breuer
Keyword(s):  
Brownian Motion ◽  
Hazard Rate ◽  
Local Times ◽  
Insurance Risk ◽  
The Matrix ◽  
Markov Modulated

We consider a Markov-modulated Brownian motion (MMBM) with phase-dependent termination rates, i.e. while in a phase i the process terminates with a constant hazard rate ri ≥ 0. For such a process, we determine the matrix of expected local times (at zero) before termination and hence the resolvent. The results are applied to some recent questions arising in the framework of insurance risk. We further provide expressions for the resolvent and the local times at zero of an MMBM reflected at its infimum.

scholarly journals Early Models Describing the Fire Insurance Risk

1979 ◽  
Vol 10 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Paul Johansen
Keyword(s):  
Risk Premium ◽  
Fire Risk ◽  
Insurance Companies ◽  
Practical Case ◽  
Insurance Risk ◽  
Life Assurance ◽  
Fire Insurance ◽  
Italian Mathematicians ◽  
Risk Rate ◽  
Image Position

It has been known for generations that the fire risk rate increases with the size of the insured object in a similar way as the death rate increases with the age.Professor d'Addario and other Italian mathematicians have shown that statistical data often can be graduated by the formulas where S denotes the sum insured:In 1940, d'Addario) in a practical case found the values α = 0.78, β = 0.44. In 1956, Blandin and Depoid have used the same formulas. Although these formulas in practical cases often lead to good approximations, one can hardly say that a proper mathematical or physical model describing the behaviour of fires lies behind.About 1950, I worked with the statistics of a group of Danish fire insurance companies, in particular covering farm buildings. This investigation was organized by Gunnar Benktander. Our data confirmed the increase of the fire risk rate with the size of the buildings.In one special group: Farm houses with thatched roofs, this increase was so important that the risk premium was approximately proportionate to the square of the sum insured. The statistics fully justified the tariffing and we tried to construct a model describing and explaining the observed facts.The risk group in question was characterized by the overwhelming importance of total or practically total losses. Only a few per cent of the damages went to minor fires. When a fire breaks out in such a building, and reaches a certain slight extent, then it is not possible to save the building from total destruction. With sufficient approximation, we may say that only total losses occur (as in life assurance).

scholarly journals On the Markov-modulated insurance risk model with tax

2010 ◽  
Vol 31 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Jiaqin Wei ◽  
Hailiang Yang ◽  
Rongming Wang
Keyword(s):  
Risk Model ◽  
Insurance Risk ◽  
Markov Modulated ◽  
Insurance Risk Model

The Resolvent and Expected Local Times for Markov-Modulated Brownian Motion with Phase-Dependent Termination Rates

2013 ◽  
Vol 50 (02) ◽  
pp. 430-438 ◽  
Author(s):  
Lothar Breuer
Keyword(s):  
Brownian Motion ◽  
Hazard Rate ◽  
Local Times ◽  
Insurance Risk ◽  
The Matrix ◽  
Markov Modulated

We consider a Markov-modulated Brownian motion (MMBM) with phase-dependent termination rates, i.e. while in a phase i the process terminates with a constant hazard rate r i ≥ 0. For such a process, we determine the matrix of expected local times (at zero) before termination and hence the resolvent. The results are applied to some recent questions arising in the framework of insurance risk. We further provide expressions for the resolvent and the local times at zero of an MMBM reflected at its infimum.

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